Question

In the diagram, mAngleFLI is 106°, mAngleFLG = (2x – 1)°,
mAngleGLH = (x + 17)°, and mAngleHLI = (4x – 15)°.

Four lines extend from point L. They are lines L F, L G, L H, and L I.
What is the measure of the smallest angle in the diagram?

15°
29°
32°
45°

Answer 1

Order the rays as F–G–H–I around L, so ∠FLI = ∠FLG + ∠GLH + ∠HLI.
(2x − 1) + (x + 17) + (4x − 15) = 106 → 7x + 1 = 106 → x = 15.

Then ∠FLG = 2x − 1 = 29°, ∠GLH = x + 17 = 32°, ∠HLI = 4x − 15 = 45°.
The smallest angle is 29°.